Step1: Prepare the Crust:

• In a large mixing bowl, whisk together the flour, salt, and sugar.
• Add the chilled butter cubes and use a pastry cutter or your hands to blend the butter into the flour mixture until it resembles coarse crumbs.
• Gradually add ice water, 1 tablespoon at a time, and mix until the dough just comes together.
• Divide the dough in half, shape each half into a disc, wrap in plastic wrap, and refrigerate for at least 1 hour.

Step2: Prepare the Filling:

• In a large bowl, combine the sliced apples, granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, allspice, and flour. Toss to coat the apples evenly.

Step3: Assemble the Pie:

• Preheat the oven to 425°F (220°C).
• Roll out one disc of dough on a lightly floured surface to fit a 9-inch pie pan. Transfer the dough to the pie pan, allowing the excess to hang over the edges.
• Pour the apple filling into the crust and dot with pieces of butter.
• Roll out the second disc of dough and place it over the filling. Trim the excess dough and crimp the edges to seal.
• Cut slits in the top crust to allow steam to escape.
• Brush the top crust with the beaten egg and sprinkle with coarse sugar if desired.

Step4: Bake the Pie:

• Place the pie on a baking sheet to catch any drips.
• Bake in the preheated oven for 45-50 minutes, or until the crust is golden brown and the filling is bubbly.
• If the edges of the crust start to brown too quickly, cover them with foil.
• Allow the pie to cool on a wire rack for at least 2 hours before serving.